Department of Health, Nutrition, and Exercise Sciences, University of Delaware, Newark, Delaware 19716; 2

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1 Journal of Strength and Conditioning Research, 2005, 19(2), National Strength & Conditioning Association Brief Review NORMALIZING PHYSICAL PERFORMANCE TESTS FOR BODY SIZE: A PROPOSAL FOR STANDARDIZATION SLOBODAN JARIC, 1 DRAGAN MIRKOV, 2 AND GORAN MARKOVIC 3 1 Department of Health, Nutrition, and Exercise Sciences, University of Delaware, Newark, Delaware 19716; 2 The Research Center, Faculty for Sports and Physical Education, Belgrade University, Serbia and Montenegro, Yugoslavia; 3 Faculty for Kinesiology, University of Zagreb, Zagreb, Croatia. ABSTRACT. Jaric, S., D. Mirkov, and G. Markovic. Normalizing physical performance tests for body size: A proposal for standardization. J. Strength Cond. Res. 19(2): There is a lack of standardized methodology for normalizing various indices of muscle strength and movement performance tests for differences in body size in human movement related disciplines. Most of the data presented in the literature have been body size dependent, which precludes both comparisons between subjects and establishment of standards for specific subject populations. The goal of the present review was to propose standardized tests that normalize physical performance tests to body size. Specifically, we propose (a) using an allometric normalization based on theoretical models that presume geometric similarity, (b) using classification of performance tests based on particular values of the allometric parameters required for normalization, and (c) using a simple performance index that represents an individual or group performance relative to a reference population. Correspondences between theory and experimental findings and limitations are discussed. KEY WORDS. scaling, allometric, muscle strength, movement INTRODUCTION Muscle strength usually refers to the force or torque of a particular muscle group developed during maximal voluntary contraction under a given set of conditions (19, 46). Some authors also refer to explosive force production as an additional class of muscle strength tests (46). Movement performance tests assess the ability to perform various functional tasks under standardized movement conditions (5; see also Table 1 for examples of muscle strength and movement performance tests). Both muscle strength and movement performance tests have often been referred to as physical performance tests. They have been used to assess muscle function, provide normative values for various groups of subjects, evaluate the success of training and rehabilitation procedures, prevent injuries, and evaluate the performance capabilities for sport- and work-related activities (5, 19, 46). Simplicity and validity have made physical performance tests popular in areas such as sports medicine, athletics, physical education, physical medicine and rehabilitation, and ergonomics. Various factors may confound physical performance tests. In addition to gender, age, level of physical activity, and skill (3, 26), body size is a well-recognized factor that affects both muscle strength and the outcome of a number of functional performance tests (20, 31). Although the role of body size has been studied for a long time (5, 31), the normalization for body size has often been inconsistently applied when presenting data from routine physical performance tests. Surprisingly, this problem was not exclusively related to the groups of tests that only recently attracted attention of researches (see further text for details), but also to the tests of muscle strength and resistance training that have been thoroughly studied for decades (19, 25, 31, 32). Therefore, most of the data presented in the professional literature has been body size dependent, while relationships among different tests have been confounded by the body size effect. Finally, comparisons of data obtained from different studies have often been invalid, which prevented researchers from establishing normative values for various tests applied on particular populations. We believe that these problems mainly originate from 2 different sources. The first is a lack of standardized methodology for the assessment of the role of body size in a given test for physical performance. The second is the neglect to consider the test-specific effects of body size. Therefore, the goal of the present study was to review both the common methods employed and the experimental findings related to the effect of body size on various physical performance tests. On the basis of the literature review, we argue for a theoretically based assessment of body size independent indices of muscle strength and movement performance and for comparing these indices with normative standards. Specifically, we propose the following: (a) using an allometric normalization method for physical performance tests based on the theoretical presumption of geometric similarity; (b) classifying physical performance tests based on the allometric parameters required for normalization; and (c) using a simple performance index that represents an individual or group performance relative to a reference population. ASSESSMENT OF THE BODY SIZE EFFECT Theoretical Approach: Effects of Scale Based on Geometric Similarity and the Resulting Allometric Parameters Muscle force and movement performance have been analyzed from a theoretical prospective to determine what role body size may play when effects of scale are considered (31). The most commonly used starting point is called geometric similarity (sometimes also called biological similarity; for details, see [8, 31]). Geometric similarity assumes that all human bodies have the same shape and that, therefore, they differ only in size. As a consequence, all lengths are proportional to a characteristic length measured on a subject (e.g., body height; L), and all areas (e.g., muscle cross-sectional area) are proportional to L 2 (body height or any other length squared), 467

2 468 JARIC, MIRKOV, AND MARKOVIC TABLE 1. Classification of selected physical performance tests based on the recommended allometric parameter. Recommended allometric parameter Groups of tests Examples of tests Recorded variable b 1 Muscle torque Strength of a muscle group recorded Torque with an isokinetic device b 2/ Muscle force Strength of a muscle group recorded Force with a dynamometer Rate of force/torque development Maximum slope of the force-time or torque-time curve Force or torque per time unit Exertion of external force Weightlifting, manual material handling Force or weight lifted Muscle power Wingate tests, power measured by an Power isokinetic device b 0 Performance of rapid move- Sprinting, jumping, throwing, kick- Velocity, movement ments Time to reach a certain relative level on the force- or torque-time curve ing, punching Time to attain 30% or time to increase force/torque between 20 and 80% of maximum voluntary contraction b 1/ Supporting body weight Maintaining difficult postures, chinups, push-ups, 1-leg raises time Time Time or number of repetitions while all volumes and volume-related indices (such as body mass or weight) are proportional to L 3. Conversely, if body mass (m, or lean body mass or any other related index) is measured, any area is proportional to m ⅔, while any length is proportional to m ⅓ (5, 15, 31). A number of important relationships have been deduced from the effects of scale that are based on the presumption of geometric similarity. For example, since muscle force is proportional to the muscle physiological crosssectional area, it should increase with body size in a manner that is proportional to m ⅔. This relationship has been often used to explain why muscle strength increases with body size at a lower rate than body mass or weight (7, 31). The torque that can be exerted about a particular joint, however, is a product of muscle force (proportional to m ⅔ ) and muscle lever arm (as any other length proportional to m ⅓ ) or m ⅔ m⅓ m. As a result, joint torque should increase at a higher rate with respect to body size than muscle force (21). Performance of a number of functional tests based on muscle actions intended to support body weight under strength-demanding conditions (e.g., maintaining difficult postures, push-ups, squats) should be negatively related to body size (19, 20). Specifically, since body weight increases in a manner that is proportional to body mass (i.e., proportionally to m 1 ; see previous text), while the muscle force needed to overcome the body weight increases at a slower rate (proportionally to m 2/3 ), the performance of this group of functional tests should be proportional to m ⅔ /m 1 or m ⅓. When applied to the analyses of complex movements that depend on power, the effect of scale provides an additional set of predictions for the relationship that exists between various physical performance measures and body size. For example, the performance of rapid movements (e.g., sprinting, jumping, throwing) should not be body size dependent, although the recorded muscle power is proportional to m ⅔ (5, 15, 31). Note that this approach often leads to normalization with respect to body size indices for power that are different from 1 (e.g., muscle force normalized with respect to body mass for power ⅔). This approach is often referred to in the literature as allometric normalization, while the assessed exponential parameter is referred to as the allometric parameter (21, 31, 44). Conversely, the normalization approach that a priori presumes a linear relationship between physical performance and body size (e.g., muscle strength or power presented per kilogram of body mass or unit of body height) is often referred to as isometric scaling (8, 31). Although the latter presumption has been heavily criticized (5, 8, 31), isometric scaling is still often applied when presenting indices of physical performance normalized for body size (19, 20). An important practical implication of these findings is that it suggests a method for normalizing tested muscle strength or movement performance. For example, if a certain performance T is proportional to m b, then the following equation provides the body size independent (or normalized) index of performance a. b a T/m (1) Despite some obvious shortcomings (see further text for details), the effect of scale that is based on the presumption of geometric similarity has been the most often employed in the literature to explain some basic findings related to the effects of body size on various physical performance tests, as well as to provide the allometric parameters for normalizing outcomes of various physical performance tests (5, 31, 34, 36). More complex scaling methods (e.g., the effect of scale that is based on the constant stress or elastic similarity [31] or nonparametric curve fitting [25]) are beyond the scope of this study. Experimental Approach: Assessment of Allometric Parameters From Individual Sets of Data The effect of body size on physical performance can be confounded by a number of factors. For example, human bodies are not identical in shape, and differences in body composition such as the percentage of total body mass comprised by muscle tissue inevitably affect the massspecific muscle strength and power observed (9, 16, 42). Performance of functional movements is also affected by maturation, aging, level of physical activity, and skill as well as a number of other factors (5, 19, 26, 35). Moreover, each of these confounding effects could affect different

3 PHYSICAL PERFORMANCE TESTS AND BODY SIZE 469 tests differently. For example, a somewhat higher percentage of fat tissue than in most other athletes could be advantageous for swimmers (28) but not for soccer players (40). Some sport-specific tests (e.g., a standard test of sprinting with a ball relevant to soccer players [9]) demand more skill than simply an exertion of maximum voluntary contraction (MVC). As a consequence, although theoretical models predict unambiguous relationships between the recorded performance for each particular test and a selected index of body size, experimental findings suggest that these relationships are also both subjectand test-specific. For example, there is ample evidence that the performance body size relationship may differ when the same test is applied to different populations (for reviews, see [19, 26, 46]). To accurately assess the performance body size relationship, a number of authors have applied an experimental approach rather than using theoretical models, such as the effects of scale based on the presumed geometric similarity that was discussed in the previous section. These empirical findings were then used to assess the body size independent (or normalized) indices of the performance on the specific populations tested. Although some methodological shortcomings have been pointed out (7, 10, 18, 25, 35), allometric scaling represents by far the most popular approach to the assessment of the relationship between various tested performances and selected indices of body size applied to individual sets of experimental data (7). Specifically, it presumes an allometric relationship: b T am (2) where T is the measure of performance, m is body mass (or, alternatively, any other index of body size), and b is the allometric parameter for the applied test. Note that the term allometric comes from the presumption that the allometric parameter does not necessarily have to be that b 1, similar to the theoretical approach described within the previous section. Interpretation of the coefficient a is discussed subsequently. The log transformation of equation 2 gives the following equation: log T log a b log m (3) where logs a and b, respectively, correspond to the values for the intercept and slope of the regression line that is fitted through the logarithmic values of the experimentally recorded m and T. Finally, the assessed value of the allometric exponent b allows the calculation of a body size independent index of the tested performance a i for each particular tested subject: ai T i/mi b (4) which corresponds to the results obtained from the normalization method based on theoretically obtained allometric parameters (equation 1). The only difference is that the specific value of the allometric parameter b is a result of the applied calculation procedure instead of being obtained through theoretical analysis. Further in the text, we will refer to a i as normalized individual performance. This performance, calculated from his/her performance T i and body size m i (equation 4), corresponds to the coefficient a (equation 1) related to the performance T and body size m for the entire group of subjects. Equations 2 and 4 are different only in that the former represents the performance body size relationship for the entire group, while the latter represents the same relationship for the individual. Therefore, the coefficient a (equation 2) represents normalized group performance. The origin and importance of any minor numerical difference between normalized group performance a and normalized individual performance a i averaged across the subjects are discussed in later sections. Note that the same method of normalizing individual performance (see equation 4) has been routinely applied in literature when presenting various data, such as a tested muscle strength or maximum oxygen consumption per kilogram of body mass, which presumes b 1, although both the theoretical and experimental findings suggest that b 1 (5, 31, 34). Conversely, according to equation 4, any instance of nonnormalized data presumes that b 0. Figure 1 illustrates the main steps of the procedure where it is applied on a selected set of data from our previous study (21). The first graph illustrates the positive relationship between the maximum isometric torque of elbow flexors recorded by means of an isokinetic dynamometer and body mass (Figure 1a). Figure 1b shows the regression line (see equation 3) generated from the logtransformed set of the previous data. This particular set of data provides a value for the allometric parameter that is very close to the value that is theoretically predicted for muscle torque (b 1; see previous section for details), while the normalized group performance is close to a 1 because of the range of test values being similar for muscle torque and body mass. Finally, Figure 1c shows the normalized individual performance where the recorded torques are normalized with respect to individual body mass according to equation 4. The data indicate no relationship with body mass, while the depicted value a corresponds to the normalized group performance. See further text for details on using a selected normalized individual performance (illustrated by a i ; Figure 1c) to assess the performance index. Finally, note that the experimentally obtained relationship between physical performance and a selected index of body size is inevitably both subject- and test-specific. Therefore, despite providing an accurate normalization for body size for that particular test and particular subject sample, this approach leads to a number of problems in the routine testing of physical performance. These problems, as well as possible solutions to them, will be discussed in the next section. Comparison of Theoretical and Experimental Findings Information in the previous section showed how important it is to study the relationship between performance and body size, not only for each particular test (as suggested by theoretical predictions) but also for each particular subject population that is tested on a specific performance task. However, there is strong evidence that, despite considerable inconsistencies in the observed data, the experimental findings observed in different subject populations on average support the theoretical predictions briefly discussed within previous sections. Further text will specifically deal with the results obtained from some of the most important groups of physical performance tests, as well as with general experience that relates to the performance of different movement tasks.

4 470 JARIC, MIRKOV, AND MARKOVIC FIGURE 1. Example of allometric scaling applied on an experimentally recorded set of data. (a) A set of data that illustrates the expected positive relationship between muscle strength and body size. (b) The log-transformed data from the previous graph that allows an assessment of the regression coefficients. (c) The same set of data normalized using the regression coefficients (see text for details). Note that the data show no relationship with body mass. The value a corresponds to the normalized group performance, while a i represents the normalized individual performance of a selected subject (indicated by arrow). Muscle Strength. Strength of a muscle group is usually assessed as either externally exerted muscle tension recorded by a dynamometer or the same tension recorded by an isokinetic apparatus as net joint torque. Although the normalization for body size has been applied inconsistently when presenting results of routine strength tests (see tables of review in [19]), both everyday experience and experimental findings suggest that a positive relationship exists between muscle strength and body size. Despite a relatively wide scatter, the values of allometric parameters obtained for torque and force when analyzing the results of tests of the same muscle groups proved to be close to the theoretically predicted values of b 1 and 0.67, respectively (19, 21). Both similar values and the distinction between the allometric parameters that we observed for muscle torque and force have been demonstrated in other studies. For example, while the maximum force exerted by specific muscle groups usually demonstrates that the value of the allometric parameter is close to b 0.5 (7, 44) or somewhat higher (23), the maximum torque often shows values either close to (10, 45) or even above b 1 (33). Explosive Force Production. Explosive force (or torque) production has been considered an additional class for tests of muscle strength (45). In addition to its usefulness as a general assessment tool for neuromuscular function, some athletic activities require that force be produced for a very short period, and this is an most important rationale for performing this kind of assessment. In addition to the often applied rate of force development (RFD), which is assessed as the maximum slope of the recorded force-time (or torque-time) curve, several other tests for explosive force production have been employed (see [46] for review). Our recent study (32) showed that some standard tests are muscle strength dependent (such as RFD, or the force exerted after a preselected time interval), while others are muscle strength independent, such as RFD/MVC or the time needed to attain a predetermined relative level of force (MVC). These findings are in line with studies that show a positive relationship between RFD and maximum muscle force (13), as well as with studies that suggest presenting RFD relative to MVC rather than absolute RFD (41). Since muscle force or torque requires particular allometric parameters to be normalized for body size (see previous paragraphs), the same values should be also used for the muscle strength dependent tests (i.e., RFD, or the force exerted after a preselected time interval) of explosive force production. Muscle strength independent tests, such as RFD/MVC, or the time needed to attain a predetermined relative level of force, however, should require no normalization (i.e., the allometric parameter should be b 0). Muscle Power. Maximum muscle power has been usually assessed as the peak product of either force and velocity or torque and angular velocity of a particular muscle group exerted against an external device (3, 38). Some tests of muscle power are also based on the joint action of several groups, such as tests performed on a bicycle ergometer. Most studies show that the value for this allometric parameter is close to the theoretically predicted value b 0.67 (for reviews, see [5, 31]). Similar values have been observed for both mean and peak power recorded during complex movements (8, 11, 17, 24, 36). Exertion of External Force. Similar to muscle strength that is recorded as a force of a tested muscle group, tests

5 PHYSICAL PERFORMANCE TESTS AND BODY SIZE 471 involving the exertion of force against external objects or devices suggest that the recorded force increases at a lower rate than does body mass. The results observed in ergonomic tasks (14), weightlifting (8, 25, 30, 43), and the 2-leg lift (1) suggest values of the allometric parameter either close to or somewhat lower than the theoretically predicted b The lower values for this parameter than for those theoretically predicted have been explained because the task involves lifting segments of the subject s body together with the recorded external weight (1, 8), as well as the existence of prominent differences in body composition of the athletes competing in the different categories of weightlifting (7). Performance of Rapid Movements. Our experience tells us that the fastest possible movements (e.g., the highest jumping, the fastest running, kicking, or throwing light objects) should be expected from neither the biggest nor the smallest individuals. Even the analysis of the maximum running velocity performed on a much broader scale of animal body sizes provides a similar result (see [31] for a review). Our recent studies of the relationship between the performance of rapid movements and body size have also shown either a weak relationship or no relationship at all between the performance of rapid body movements and body size (1, 30, 42). These results in general support theoretical predictions based on the effect of scale and presumption of geometric similarity (5, 15) and, therefore, suggest that b 0 for the normalization of this group of physical performance tests. Supporting Body Weight. A number of movements and postures require high muscle forces to overcome body weight. Examples are some standard movement performance tests (e.g., push-ups, chin-ups, squats, and 1-leg lifts), some strength-demanding postures (keeping back horizontally extended), and the keeping of some difficult position in gymnastics or yoga. Experimental results, in general, suggest that lighter subjects demonstrate worse results in exerting external force but are better when performing tasks that require them to overcome their own weight (6, 39). The small stature displayed by elite acrobats and gymnasts is a well-known phenomenon (4, 12). Recent experimental findings suggest that the performance body size relationship for this group of tasks is negative, while the corresponding allometric parameter should be close to the theoretically predicted b 0.33 (1, 30) (see previous sections for theoretical predictions). To conclude, there is no question that experimental assessments of the allometric parameter b for each particular test performed with a particular group of subjects provides an accurate assessment of the body size independent index of performance (see equations 2 4 and Figure 1 as an example). However, this procedure has several shortcomings when it is performed in a standardized fashion on each set of data obtained in routine comprehensive tests of physical performance. First, the procedure per se is quite time- and effort-demanding. Second, using different allometric parameters for the same test when applied to different populations would prevent professionals from both establishing standards and comparing different subject populations. Also taking into account arbitrarily applied normalization for body size that occurs in contemporary literature (e.g., different normalizations applied to the same tests in different studies, different normalizations applied on the same set of data, or even no normalization applied at all) (for reviews, see [19, 23]), it becomes apparent that the testing of physical performance requires standardized methods when normalizing performance to body size. Despite some inconsistencies, the main finding, given on the experimental results reviewed within this section, is that the relationship between physical performance and body size is generally in line with the theoretical predictions discussed in previous sections. Thus, instead of experimental assessment, we propose using allometric parameters that are based on theoretical predictions for the effect of scale and geometric similarity. This method of normalization for body size should be applied when reporting results of routine tests of physical performance in various human movement related areas. In addition to both a standardization and simplification of the testing procedures, this approach would allow a comparison of the results obtained in different studies and would establish standards for comparison (see further text for details). CLASSIFICATION OF THE TESTS BASED ON RECOMMENDED ALLOMETRIC PARAMETERS Basic Groups of Tests Despite the expected simplification and standardization, the diversity of tests applied in areas such as physical education, sports, ergonomy, and physical medicine and rehabilitation could continue to be a problem when normalization for body size is attempted. A literature review shows an immense number of different physical performance tests, as well as major differences in methodologies when these tests are applied in different fields or on different populations. This complexity seems to make the task of the discussed standardization particularly challenging. However, both theoretical analysis that is based on the effect of scale and actual observed experimental findings suggest that a number of different physical performance tests require the same allometric exponent b; (see equations 1 and 4). For example, the previous sections did not discuss particular tests, but rather, groups of tests. Table 1 illustrates a proposed classification scheme for selected physical performance tests from the perspective of the effect of body size. The current classification is based on a restructured table of our recent proposal (20), with the addition of the tests for muscle power and the tests for explosive strength production. The classification of all selected tests is based on only 4 recommended values for the allometric parameter b {1; 0.67; 0; 0.33}. It is also important to stress that the proposed classification implies that the allometric parameter b is test-specific but not subject-specific. However, we believe that the currently proposed classification scheme is only a starting point for further research, since a number of physical performance tests have not been included, and both the suggested classification of tests and the corresponding allometric values require further evaluation (see further sections for details). Relationship Between 2 Different Tests Physical performance testing is often based on the implicitly presumed relationship between muscle strength and movement performance. For example, muscle strength is often tested to predict athletic performance, while neurological patients are tested for functional movement tasks to assess their neuromuscular function

6 472 JARIC, MIRKOV, AND MARKOVIC (19, 27, 33, 46). Recent reviews have shown that the role that body size plays has been neglected when assessing the relationship between 2 physical performance tests (19, 20). Both the proposed normalization method and particular values of the allometric parameter (see Table 1) allow not only the calculation of the body size independent indices of various physical performance tests, but also the assessment of the relationship between the results of 2 different tests not confounded by the effect of body size. For example, let us assume that a performance T 1 is assessed from a tested performance T 2 : T1 T2 (5) To avoid the possible confounding effect of body size, both tests should be normalized using equation 1, which gives the following: b1 b2 T /m T /m 1 2 (6) where m is the subjects body mass, and b 1 and b 2 are the recommended allometric parameters (see Table 1) for normalizing the tested performance T 1 and T 2, respectively, for body size. Finally, equation 6 gives the following: T1 T 2 /m b2 b1 (7) The last equation suggests that the relationship between 2 physical performance tests should take into account the role that body size plays in both of them. For example, if the maximum force of elbow flexors (test T 1, equation 7) is assessed by the maximum number of chinups (test T 2 ), the force should be divided by m 1 (or, alternatively, multiplied by m 1 ), since the exponential value of equation 6 should be b 2 b (see Table 1). However, the assessment of the forces of active muscles from the results of the maximum weight lifted requires no normalization because the same allometric parameter is recommended in both tests, which gives m b2 b1 m m 0 1. PROPOSAL OF THE PERFORMANCE INDEX One of the important purposes of the tests under discussion is that they facilitate the profiling of specific groups of subjects (e.g., schoolchildren vs. elderly persons, athletes of different specializations, various groups of patients [5, 12, 22, 46]). These profiles are thereafter used as standards to assess the relative strengths or performances of either individuals or particular subpopulations. However, it has been already pointed out that the obtained standards have often been presented using either incorrect normalizations for body size or even no normalization at all, not to mention the fact that comparison of individual results with the standards has rarely included the possible effect of body size. Therefore, assessments of individual results with respect to the established standards have often been unreliable because of the application of either erroneous or different normalization methods. The suggested normalization method (equation 1), as well as the 4 default values for the allometric parameters recommended for particular types of tests (see Table 1), provides an opportunity to propose a relatively simple performance index that could be used to present the results obtained for a particular subject or, alternatively, for a group of subjects relative to standard performance. We will illustrate the proposed procedure as applied to the set of data from our previous study (21). Let us assume that the depicted normalized group performance a (see Figure 1c) is generally accepted as a standard performance for this particular test when applied to a particular population (e.g., school students of certain age and gender or elite athletes of a particular specialization). Therefore, we want to compare any particular subject from the depicted sample or, alternatively, from another group of subjects that belongs to the same population with a standard performance. We propose a simple performance index p i that represents the ratio between the normalized individual performance a i and the normalized group performance a that has been selected to be a standard performance (both represented in Figure 1c) for this particular test and the particular subject population: pi a i /a (8) b Replacing a i with T i / m i (equation 1 applied to that particular subject) finally gives the following: pi T i/a mi b (9) Equation 9 suggests that the assessment of physical performance in the future could be based on the default values of a test-specific allometric parameter b (provided by the comprehensive classification of the specified test; see Table 1 for illustration), as well as on the subjectspecific normalized group performance a obtained from a particular sample of subjects and generally accepted as the standard performance. Therefore, only the recorded individual performance (T i ) and body size (m i ) would be required to calculate a performance index that shows to what degree the performance of the tested individual is better or worse then the standard performance (i.e., p i 1orp i 1, respectively, if higher value of T indicates better performance). Note that the proposed approach could be used not only when comparing a single subject, but also when comparing the performance of any tested group of subjects with the standard performance. In the latter case, the performance index would be calculated from the averaged individual performance T i and the averaged index of body size m i (see equation 9). LIMITATIONS Several well-known limitations in areas that are related to the testing of movement abilities could also represent significant limitations to our proposed standard. The most important ones belong to the already mentioned confounding effects that affect the tested performance, the selected index of body size, or both. Body composition or, more specifically, percentage of fat could be a major confounding factor for the increasingly obese populations of developed countries. On the other hand, elite athletes are rarely obese, so the major confounding factors that affect this performance body size population could be the early selection of athletes based on particular body shape and muscle structure or specific effects of the applied training (2, 5, 37). Our focus has been on a group of performance tests where the result of the subject s maximal effort is measured as either a physical variable (e.g., movement velocity, time duration, length of jump) or a number (e.g., number of repetitions). However, it remains unclear how to manipulate the data for the body size effect and establish

7 PHYSICAL PERFORMANCE TESTS AND BODY SIZE 473 standards in other areas where performance is based on movement skills, endurance, or even some subjective aesthetic criteria (e.g., figure skating). In this instance, some standard tests may in part belong to several different groups of the proposed classification and, therefore, require a value of the allometric parameter to be somewhat different from those recommended values. For example, a weightlifter lifts not only an external weight (belongs to the class force exerted on external objects ; b 0.67; see Table 1), but also segments of his/her own body ( supporting body weight ; b 0.33). As a result, the allometric parameter could be somewhere between these 2 values, which is also in line with some experimental findings (7, 25, 43). A similar problem could exist when the focus is on kicking and throwing performances, since the ball could be considered an external weight (suggesting b 0.67), while the rapid limb movements require b 0 (see Table 1). It should also be mentioned that the relationships among different physical performance tests, as well as between the physical performance tests and body size, are known to be on average moderate (19, 27, 29, 33, 42, 46) and, as mentioned previously, subject-specific. Therefore, their integration with the theoretical approach is not straightforward with respect to the discussed relationships and specific values of the allometric parameter. However, this problem could also support an argument for focusing more on theoretical predictions than on relatively inconsistent experimental findings when selecting standardized normalization methods. Finally, because of the nonlinear transformation of recorded performance and body size (see equations 2 4; see also Figure 1c), the assessed normalized group performance a does not exactly correspond to the normalized individual performance a i averaged across the subjects. This discrepancy could cause a difference between the index of performance calculated for an individual and the index of performance calculated for a group of individuals. Note, however, that this discrepancy should be rather small due to a relatively narrow range of both the recorded performance and body size. For example, we compared several normalized group performances recorded on the same group of subjects that had participated in our previous study (21) with the individual normalized performance averaged across the subjects. The results showed the difference to be well below 1% of the calculated values in each of the 12 sets of data. PRACTICAL APPLICATIONS The purpose of this study was both to review and evaluate the most often applied methods for calculating body size independent indices of physical performance (such as muscle strength or movement performance) in various human movement related areas. We propose the following equation: a T/m b for normalizing the tested performance T for differences in body mass m or, alternatively, any other index of body size. However, we strongly recommend using the theoretically predicted values of the allometric parameter b instead of those obtained experimentally from each particular test and group of subjects. For example, these values should be b 1 for muscle torque, b ⅔ for the exertion of muscle force and muscle power, b 0 for the performance of rapid movements, and b ⅓ for tests of supporting body weight or keeping difficult postures. Acceptance of the standardized theoretical values would not only simplify testing procedures and presentation of the obtained results, but would also allow a comparison of the data across many different studies. Finally, the recommended approach would allow the establishment of a universally accepted standard performance (normalized performance a obtained on a selected population) that could serve for the calculation of a performance index (the ratio between the normalized performance tested on a particular group of subjects and the standard performance). Therefore, we believe that there is an apparent need for handbooks of physical performance testing in various applied areas, such as physical medicine and rehabilitation, sports, physical education, and ergonomy. In addition to a comprehensive list and description of the most often applied tests, these handbooks should contain the testspecific allometric parameter b and the subject-specific standard performance a to aid in the calculation of the performance index. REFERENCES 1. AASA, U., S. JARIC, M. BARNEKOW-BERGKVIST, AND H. JOHANS- SON. Muscle strength assessment from functional performance tests: Role of body size. J. Strength Cond. Res. 17: ABERNETHY, P.J., J. JURIMAE, P.A. LOGAN, A.W. TAYLOR, AND R.E. THAYER. Acute and chronic response of skeletal muscle to resistance exercise. Sports Med. 17: ABERNETHY, P., G. WILSON, AND P. LOGAN. Strength and power assessment. Issues, controversies and challenges. Sports Med. 19: ANDERSSON, E., L. SWARD, AND A. THORSTENSSON. Trunk muscle strength in athletes. Med. Sci. Sports Exerc. 20: ASTRAND, P.-O., AND K. RODAHL. Textbook of Work Physiology (3rd ed.). New York: McGraw-Hill, BARNEKOW-BERGKVIST, M., G. HEDBERG, U. JANLERT, AND E. JANSON. Development of muscular endurance and strength from adolescence to adulthood and level of physical capacity in men and women at age of 34 years. Scand. J. Med. Sci. Sports 6: BATTERHAM, A.M., AND K.P. GEORGE. Allometric modelling does not determine a dimensionless power function ratio for maximal muscular function. J. Appl. Physiol. 83: CHALLIS, J.H. Methodological report: The appropriate scaling of weightlifting performance. J. Strength Cond. Res. 13: COMETTI, G., N.A. MAFFIULETTI, M. POUSSON, J.C. CHATARD, AND N. MAFFULLI. Isokinetic strength and anaerobic power of elite, subelite and amateur French soccer players. Int. J. Sports Med. 22: DAVIES, M.J., AND G.P. DALSKY. Normalizing strength for body size differences in older adults. Med. Sci. Sports Exerc. 29: DRISS, T., H. VANDEWALLE, AND H. MONOD. Maximal power and force-velocity relationships during cycling and cranking exercises in volleyball players. J. Sports Med. Phys. Fitness 38: FARIA, I.E., AND E.W. FARIA. Relationship of the anthropometric and physical characteristics of male junior gymnast to performance. J. Sports Med. 29: HAFF, G.G., M. STONE, H.S. O BRYANT, C.DINAN, AND R. JOHN- SON. Force-time dependent characteristics of dynamic and isometric muscle actions. J. Strength Cond. Res. 11:

8 474 JARIC, MIRKOV, AND MARKOVIC 14. HATTORI, Y., Y. ONO, M. SHIMAOKA, S. HIRUTA, E. SHIBATA, S. ANDO, F.HORI, AND Y. TAKEUCHI. Effects of box weight, vertical location and symmetry on lifting capacities and ratings on category scale in Japanese female workers. Ergonomics 43: HILL, A.V. The dimensions of animals and their muscular dynamics. Sci. Prog. 38: HULENS, M., G. VANSANT, R. LYSENS, A.L. CLAESSENS, E. MULS, AND S. BRUMAGNE. Study of differences in peripheral muscle strength of lean versus obese women: An allometric approach. Int. J. Obes. 25: IZQUIERDO, M., K. HAKKINEN, A. ANTON, M. GARRUES, J. IBA- NEZ, M. RUESTA, AND E.M. GOROSTIAGA. Maximal strength and power, endurance performance, and serum hormones in middle-aged and elderly men. Med. Sci. Sports Exerc. 33: JACKSON, A. Strength measurement: Controlling for individual differences. JOPERD 57: JARIC, S. Muscle strength testing: The use of normalization for body size. Sports Med. 32: JARIC, S. Role of body size in the relation between muscle strength and movement performance. Exerc. Sport Sci. Rev. 31: JARIC, S., S. RADOSAVLJEVIC-JARIC, AND H. JOHANSSON. Muscle force and muscle torque in humans require different methods when adjusting for differences in body size. Eur. J. Appl. Physiol. 87: JARIC, S., D. UGARKOVIC, AND M. KUKOLJ. Anthropometric, strength, power and flexibility variables in elite male athletes: Basketball, handball, soccer and volleyball players. J. Hum. Movement Stud. 40: JARIC, S., D. UGARKOVIC, AND M. KUKOLJ. Evaluation of methods for normalizing strength in elite and young athletes. J. Sports Med. Phys. Fitness 42: JENSEN, R.L., P.S. FREEDSON, AND J. HAMILL. The prediction of power and efficiency during near maximal rowing. Eur. J. Appl. Physiol. 73: KAUHANEN, H., P.V. KOMI, AND K. HAKKINEN. Standardization and validation of the body weight adjustment regression equations in Olympic weightlifting. J. Strength Cond. Res. 16: KEATING, J.L., AND T.A. MATYAS. The influence of subject and test design on dynamometric measurements of extremity muscles. Phys. Ther. 76: KUKOLJ, M., R. ROPRET, D.UGARKOVIC, AND S. JARIC. Anthropometric, strength and power predictors of sprinting performance. J. Sports Med. Phys. Fitness 39: LEAKE, C.N., AND J.E. CARTER. Comparison of body composition and somatotype of trained female triathletes. J. Sports Sci. 9: LIETZKE, M.H. Relation between weight-lifting totals and body weight. Science 124: MARKOVIC, G., AND S. JARIC. Movement performance and body size: The relationship for different groups of tests. Eur. J. Appl. Physiol. 92: MCMAHON, T.A. Muscles, Reflexes and Locomotion. Princeton, NJ: Princeton Press, MIRKOV, D., A. NEDELJKOVIC, S. MILANOVIC, AND S. JARIC. Muscle strength testing: Evaluation of tests of explosive force production. Eur. J. Appl. Physiol. 91: MURPHY, A.J., AND G.J. WILSON. Poor correlations between isometric tests and dynamic performance: Relationship to muscle activation. Eur. J. Appl. Physiol. 73: NEDER, J.A., L.E. NERY, A.C. SILVA, S. ANDREONI, AND B.J. WHIPP. Maximal aerobic power and leg muscle mass and strength related to age in non-athletic males and females. Eur. J. Appl. Physiol. 79: NEVILL, A.M., R.L. HOLDER, A.BAXTER-JONES, J.M. ROUND, AND D.A. JONES. Modeling developmental changes in strength and aerobic power in children. J. Appl. Physiol. 84: NEVILL, A.M., R. RAMSBOTTOM, AND C. WILLIAMS. Scaling physiological measurements for individuals of different body size. Eur. J. Appl. Physiol. 65: RUBY, B.C., AND R.A. ROBERGS. Gender differences in substrate utilization during exercise. Sports Med. 17: SALE, D.G. Testing strength and power. In: Physiological Testing of the High-Performance Athlete. J.D. MacDougal, H.A. Wenger, and H.J. Green, eds. Champaign, IL: Human Kinetics, pp SCHMIDT, W.D. Strength and physiological characteristics of NCAA division III American football players. J. Strength Cond. Res. 13: SHEPHARD, R.J. Biology and medicine of soccer: An update. J. Sports Sci. 17: SLEIVERT, G.G., AND H.A. WENGER. Reliability of measuring isometric and isokinetic peak torque, rate of torque development, integrated electromyography, and tibial nerve conduction velocity. Arch. Phys. Med. Rehabil. 75: UGARKOVIC, D., D. MATAVULJ, M. KUKOLJ, AND S. JARIC. Standard anthropometric, body composition, and strength variables as predictors of jumping performance in elite junior athletes. J. Strength Cond. Res. 16: VANDERBURGH, P.M., AND C. DOOMAN. Considering body mass differences, who are the world s strongest women? Med. Sci. Sports Exerc. 32: VANDERBURGH, P.M., M.T. MAHAR, AND C.H. CHOU. Allometric scaling of grip strength by body mass in college-age men and women. Res. Q. Exerc. Sport 66: WEIR, J.P., T.J. HOUSH, G.O. JOHNSON, D.J. HOUSH, AND K.T. EBERSOLE. Allometric scaling of isokinetic peak torque: The Nebraska Wrestling Study. Eur. J. Appl. Physiol. 80: WILSON, G.J., AND A.J. MURPHY. The use of isometric tests of muscular function in athletic assessment. Sports Med. 22: Acknowledgments The authors wish to thank Drs. Simon Goodman and James Richards for valuable comments and suggestions as well as their coworkers in previous studies for fruitful discussions. This study was supported in part by a CRD grant through the University of Delaware, a Serbian Research Council grant (1758), and a grant from Croatian Ministry of Science and Technology ( ). Address correspondence to Dr. Slobodan Jaric, jaric@udel.edu.